Pair truncation for rotational nuclei: j=(17/2 model

Halse, P.; Jaqua, L.; Barrett, B. R.

doi:10.1103/physrevc.40.968

Cited by 14 publications

(5 citation statements)

References 18 publications

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“…Since the SDPSM is also built up from SD pairs, it is expected that the SDPSM can produce similar results to those of the IBM. Our previous work show that the vibrational, rotational, and gamma-soft spectra can be well reproduced [49] similar to the U(5), SU (3) and SO (6) limiting spectra in the IBM. What's more, the vibrational-rotational phase transition for identical system can also be produced within the framework of the SDPSM with fermionic degrees of freedom [50].…”

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confidence: 65%

Quantum phase transitional patterns in theSD-pair shell model

et al. 2009

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Patterns of shape-phase transition in the proton-neutron coupled systems are studied within the SD-pair shell model. The results show that some transitional patterns in the SD-pair shell model are similar to the U (5) − SU (3), U (5) − SO(6) transitions with signatures of the critical point symmetry of the interacting boson model. PACS numbers: 21.60.Cs * Electronic address: luoya@nankai.edu.cn Recently, based on the Generalized Wick Theory[1], a nucleon-pair shell model(NPSM) was proposed[2], in which nucleon pairs with various angular momenta are used as building blocks. Since modern computers fail for the calculation in the full shell model space for the medium weight and heavy nuclei, some truncation scheme need to be used. The tremendous success of the interacting boson model (IBM) [3], suggests that S and D pairs play a dominant role in the spectroscopy of low-lying nuclear modes [4, 5, 6]. Therefore, one normally truncates the full shell-model space to the collective S-D pair subspace in the NPSM. The latter is called the SD-pair shell model(SDPSM)[2, 7, 8]. A crucial point in the SDPSM is the validity of the S-D pair truncation. In Ref.[9], shell model foundations of the IBM was reviewed by Iachello, the results seem to indicate that the S-D pair truncation is a reasonable approximation to the full shell model space. Thisproblem was also studied in [10,11,12] with the conclusion that the S-D pair subspace works well in the vibrational region, but in the deformed region, the inclusion of G pairs is crucial.But Dr. Zhao's work [13,14] show that the essential properties within the full shell model space survive in the S-D pair subspace. What's more, if a pure quadrupole-quadrupole interaction and a reasonable collective S-D-pair were used, the rotational behavior can be

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confidence: 65%

Quantum phase transitional patterns in theSD-pair shell model

et al. 2009

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“…(24) AtApt~0) -+ (b~b~~+z~b'tbJ)~0). mb A&t -+ b&~-2 ) tr (ApA&~A"At)b&tbt"b Ap, u T -+ 2tr ) (A TAp)bt bp cxP (20) The operators are then clearly finite; on the other hand they are just as clearly non-Hermitian. From a computational viewpoint non-Hermiticity is only a minor barrier, but it is an obstacle to an understanding of the microscopic origin of Hermitian IBM Hamiltonians.…”

Section: A Brief History Of Boson Mappingsmentioning

confidence: 99%

“…We take the simple mapping of fermion states into boson states I+~)~l~~) = 6, ' I0), (41) where the bt are boson creation operators. We construct boson operators that preserve matrix elements, introducing boson operators 7~, V~, and most importantly, the norm operator A'gy such that (4 I 7a I@p) = (@ I T I4'p), (46) where the colons ":" refer to normal-ordering of the boson operators, and CI, --2":trP": is the kth-order Casimir of SU (20), with P = P bt 6 A At (the trace is over the matrices and not the boson Fock space). This norm operator, which takes into account the exchange terms in the BZ expansion of a fermion pair given in (14), is found in Ref.…”

Section: Matrix Elementsmentioning

confidence: 99%

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Unified theory of fermion pair to boson mappings in full and truncated spaces

Ginocchio

Johnson

1995

Phys. Rev. C

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After a brief review of various mappings of fermion pairs to bosons, we rigorously derive a general approach. Following the methods of Marumori and Otsuka, Arima, and Iachello, our approach begins with mapping states and constructs boson representations that preserve fermion matrix elements. In several cases these representations factor into 6nite, Hermitian boson images times a projection or norm operator that embodies the Pauli principle. We pay particular attention to truncated boson spaces, and describe general methods for constructing Hermitian and approximately Gnite boson image Hamiltonians.This method is akin to that of Otsuka, Arima, and Iachello introduced in connection with the interacting boson model, but is more rigorous, general, and systematic.PACS number(s): 03.65.Ca, 21.60.n

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“…The Hamiltonian (with some adjustable parameters) has been approximated by the spherical single-particle energy term and terms of residual interactions consisting of the monopole, quadrupole pairing and quadrupole-quadrupole interaction between like valence nucleons and quadrupole-quadrupole interaction between valence protons and neutrons. The structure of the S pair was determined by solving the Bardeen-Cooper-Schriefer equation and the D pair is related to the S pair via a commutation with a quadrupole operator [27].…”

Section: Introductionmentioning

confidence: 99%

Structure of even- and odd-A1p0f-shell nuclei in the collective pair approximation

Kwasniewicz

Brzostowski

Hetmaniok

2003

J. Phys. G: Nucl. Part. Phys.

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The structure of A = 59-62 nuclei has been studied in the framework of the collective pair approximation. The collective pairs, determined by diagonalizing the shell-model Hamiltonian in the space of two valence nucleons occupying the 1p 1/2 , 1p 3/2 and 0f 5/2 subshells above the closed subshell 0f 7/2 of the 1p0f shell, have been considered as building blocks to describe nuclei with 2n or 2n + 1 valence nucleons in terms of n pairs or n pairs coupled with one nucleon, respectively. It is shown that the low-lying spectra of A = 59-62 nuclei can be described quite well by considering only a selected subset of all possible collective pairs.

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Pair truncation for rotational nuclei: j=(17/2 model

Cited by 14 publications

References 18 publications

Quantum phase transitional patterns in theSD-pair shell model

Quantum phase transitional patterns in theSD-pair shell model

Unified theory of fermion pair to boson mappings in full and truncated spaces

Structure of even- and odd-A1p0f-shell nuclei in the collective pair approximation

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